CN105678086A - Alternate iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption - Google Patents

Abstract

The invention discloses an alternate iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption. First, a linearization scheme is provided for calculation of a concentration field, an original system is semi-linearized, and thus the nonlinearity of the original system is weakened; then, an alternate iteration scheme is provided for the temperature field and the concentration field to be measured, and a half of the number of unknown variables is reduced in each iteration; finally, a penalty term is introduced through an optimization technology to overcome the morbidity in the reconstruction process, regularization parameters can be adjusted automatically in each iteration, and it is guaranteed that an iterative solution converges to an exact solution. According to the alternate iterative scheme, on the premise of maintaining reconstruction precision, the computing time can be shortened remarkably, and the alternate iterative algorithm is suitable for large-scale field inversion computation.

Description

Alternate iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption

Technical Field

The invention relates to an alternating iteration algorithm for temperature field and concentration field reconstruction based on spectral absorption, and belongs to the field of laser absorption spectroscopy.

Background

In recent years, with the increasing importance of the country on environmental protection and the need for ensuring the safe and efficient implementation of industrial production, the development of optical non-contact gas detection technology is rapid. The gas detection technology based on the laser absorption spectrum has the advantages of no need of pretreatment, quick response, accurate data, simultaneous detection of multiple parameters and the like, and becomes one of field online detection technologies applied to numerous fields at present.

The absorption spectrum technology uses laser to penetrate through a flow field area to be measured, when the laser frequency is the same as the transition frequency of a gas absorption component, laser energy is absorbed, an absorption value along a light path can be obtained by comparing the incident light intensity with the transmission light intensity, and then physical parameters such as gas temperature and concentration are determined. However, the measurement result of the laser absorption spectroscopy technology reflects the temperature or concentration average value of a region, and is not suitable for the measurement environment with a remarkable temperature and concentration gradient. Therefore, the method for exploring and developing the non-uniform flow field parameter measurement method based on the absorption spectrum technology has important significance.

At present, scientific research institutions at home and abroad carry out certain research on the non-uniform field parameter distribution measurement of the high-temperature reaction flow, and the measurement method based on different principles has advantages and disadvantages. The limited range direct reconstruction method utilizes the basis function to disperse the region to be detected, is suitable for a flow field with smooth distribution and is not suitable for the condition that the region to be detected has mutation. The filtered back-projection algorithm can obtain a high-precision reconstruction result under a large amount of projection light and a uniform projection angle, but the angle and the number of the projection light in actual combustion field measurement are limited by space availability and system complexity. The algebraic iterative algorithm is an optimization algorithm based on an iterative solution strategy, can be used for incomplete projection data or the situation that projections are in non-uniform distribution, has high calculation speed, but needs to increase the number of projections in different directions and cannot utilize the information of a plurality of absorption spectral lines at the same time. The sequential quadratic programming algorithm has overall convergence, keeps local convergence for more than 1 time, is high in search efficiency, is sensitive to initial value abnormality, is easy to fall into local optimum, and cannot obtain a global optimum solution. The simulated annealing algorithm improves the accuracy and stability of the temperature field and concentration field reconstruction results by increasing the measured value of the gas absorption spectrum line on the single light path, the overall reconstruction effect is superior to that of the algorithm, but the simulated annealing algorithm belongs to a random search optimization algorithm, the calculation efficiency is low, and the time consumption is too long.

Disclosure of Invention

The invention aims to provide an alternating iterative algorithm for reconstructing a temperature field and a concentration field based on spectral absorption.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows:

an alternating iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption, comprising the following steps:

step one, allowing the high-temperature gas to be measured to flow through a two-dimensional rectangular area, and recording the area to be measured as D { (x, y): 0 < X < L, 0 < y < W }, a temperature field T (X, y), a concentration field X (X, y), and a relationship between a laser measurement value passing through the region D and the temperature field and the concentration field in the region D is expressed by equation (1):

in the formula, A (y)₀，v₀) Is a center frequency v₀Along a path y ═ y₀∈ (0, W) integrated absorption area measurement, B (x)₀，v₀) Is along path x ═ x₀∈ (0, L), P is the gas pressure over region D, S (T (x, y)₀)，v₀) Is a temperature T (x, y)₀) Frequency v₀The spectral line of (A) is strong;

step two, solving (X (X, y), T (X, y)) according to the formula (1):

1) suppose (X)^*(x，y)，T^*(X, y)) is an exact solution that satisfies the system, while giving (X)^*(x，y)，T^*(x, y)) is a priori approximatedAnd an iteration initial value (X)⁰(x，y)，T⁰(x, y)), and gives the maximum number of iterations N_maxRegularization parameters μ, β > 0, iteration termination level > 0, and an allowable set X_range×T_rangeSetting the initial value of n to be 0;

2) for known Tⁿ(X, y) X is obtained by solving the following formula through post-discretization regularizationⁿ⁺¹(x，y)：

In the formula,an operator used in the iteration is represented; if Xⁿ⁺¹(x，y)∈X_rangeTaking mu as mu₀And jumping out of this iteration; otherwise, update μ ← 2 μ, calculate X againⁿ⁺¹(x，y)；

3) For known Xⁿ⁺¹(x, y) T is obtained by solving the following formula through post-discretization regularizationⁿ⁺¹(x，y)：

In the formula,an operator used in the iteration is represented; if Tⁿ⁺¹(x，y)∈T_rangeChoose β ═ β₀And jump out of the iteration, otherwise update β ← 2 β, calculate T againⁿ⁺¹(x，y)；

4) For a sufficiently large number n, the termination criterion is satisfied:

||(Xⁿ⁺¹，Tⁿ⁺¹)-(Xⁿ，Tⁿ)||_D＜(4)；

or N ═ N_maxThe iteration terminates, (X)ⁿ⁺¹，Tⁿ⁺¹) As final solutions of concentration field and temperature field; otherwise, updating Tⁿ←Tⁿ⁺¹N ← n +1, and steps 2) to 4) are repeated.

In order to improve the reconstruction effect, the invention provides that in each direction of the area to be measured, the information comprising a plurality of gas characteristic absorption spectral lines is fully utilized, and the center frequency corresponding to the r-th gas characteristic absorption spectral line is selected and recorded as v_rThe formula (2.1), the formula (2.2), the formula (3.1), the formula (3.2) and (A, B) depend on v_rThus, each iteration of the steps in equations (2.1), (2.2), (3.1) and (3.2) may be replaced by equations (5.1), (5.2), (6.1) and (6.2), respectively:

carrying out grid discretization treatment on a two-dimensional area to be detected, and solving the concentration and the temperature in each grid by adopting a self-adaptive iteration method, namely Xⁿ⁺¹(x, y) and Tⁿ⁺¹(x，y)：

1) Dividing the two-dimensional area to be measured into M rows and N columns of grids according to the shape and the size of the two-dimensional area to be measured D, enabling M to be equal to N, enabling each grid to correspond to a value to be measured of concentration and temperature, selecting I gas characteristic absorption spectral lines from a spectral database, and enabling I to be more than or equal to [2 XMXN/(M + N) ], wherein the value of r is an integer between 1 and I;

2) equation (5.2) is written as:

EgS(T，v_r)X＝P(v_r)(7)；

in the formula, P (v)_r) Is a spectral line v_rCorresponding measured value projection vector, E ═ E (E: (a), (b), and (c) (c))_i，j)) Is 2N × N²0-1 matrix of dimensions, where e_(i，j)Indicating whether the laser passes through the jth lattice in the ith direction; namely the firstWhen the laser in i directions passes through the jth grid, let e_(i，j)1, otherwise e_(i，j)＝0；

The explicit solution of equation (7) is represented as:

wherein,

by formula (8) of Tⁿ(X, y) calculating to obtain Xⁿ⁺¹(x，y)；

3) X calculated in step 2)ⁿ⁺¹(x, y) as a known quantity, and solving equation (6.1) using a nonlinear least squares optimization algorithm to obtain Tⁿ⁺¹(x，y)。

Wherein in order to ensure numerical convergence of the iterative solution, an allowable set X of X (X, y) and T (X, y) is given_range×T_rangeSo that it contains the exact solution X^*(x, y) and T^*(x, y) and simultaneously introducing a penalty term with the regularization parameters mu and β to overcome the ill-conditioned nature of the reconstruction process, and automatically adjusting the regularization parameters mu and β in each step of iteration so as to ensure that the iterative solution converges to an accurate solution.

Has the advantages that: the algorithm can solve the problem of nonlinearity when the temperature field and the concentration field are reconstructed by adopting absorption spectrum data, and simultaneously overcomes the ill-posed characteristic in the reconstruction process by introducing a punishment item by utilizing an optimization technology, thereby not only fully utilizing multispectral measurement information, but also obviously shortening the calculation time while ensuring the reconstruction quality.

Drawings

FIG. 1 is a flow chart of the algorithm of the present invention;

FIG. 2 is a schematic diagram of the meshing of the region to be measured in the algorithm of the present invention;

FIG. 3 is a diagram of a concentration field model set in a simulation embodiment of the present invention;

FIG. 4 is a model diagram of the temperature field set in a simulation embodiment of the present invention;

FIG. 5 is a graph of the results of the algorithm reconstruction of the concentration field of the present invention;

FIG. 6 is a graph of the results of the algorithm reconstruction of the temperature field of the present invention;

FIG. 7 is a graph of the results of a simulated annealing algorithm reconstructing a concentration field;

FIG. 8 is a graph of the results of a simulated annealing algorithm reconstructing a temperature field;

FIG. 9 is a root mean square error plot of the reconstructed temperature field at different noise levels for the proposed algorithm and simulated annealing algorithm.

Detailed Description

The present invention is described in detail below with reference to the attached drawings.

As shown in FIG. 1, the alternating iterative algorithm for reconstructing the temperature field and the concentration field based on spectral absorption of the present invention comprises the following implementation steps:

step one, supposing that the high-temperature gas to be measured flows through a two-dimensional rectangular region, lasers with different frequencies enter from the side face of the region, and corresponding lasers absorbed by the gas are obtained on the opposite face, wherein the region to be measured is expressed as D { (x, y): x is more than 0 and less than L, y is more than 0 and less than W, the temperature field is T (X, y), the concentration field is X (X, y), and the central frequency corresponding to the adopted gas characteristic absorption spectrum line is v₀. Along the optical path y ═ y₀∈ (0, W) the energy absorption is expressed as:

in the formula, I (L, y)₀，v₀) Is along y ═ y₀The transmitted light intensity obtained at x-L corresponds to the incident light intensity I (0, y) of the laser light₀，v₀)；α(y₀，v，v₀) The incident laser light is on the path y ═ y₀Absorbance of (d); p is the gas pressure over region D; phi (v-v)₀) Is a value of a linear function corresponding to the selected spectral line at a frequency v, is selected from one of a Gauss line type, a Lorentz line type and a Voigt line type according to conditions of temperature and pressure in a measurement environment, and satisfiesS(T(x，y₀)，v₀) Is a temperature T (x, y)₀) Frequency v₀The spectral line of (a) is strong and can be expressed as:

in the formula, the reference temperature T₀296K, h is planck's constant, c is the speed of light, E "is the low state energy level, and K is the boltzmann constant. The molecular partition function q (t) is approximately described as:

Q(T)＝a+bT+cT²+dT³(3)；

the coefficients (a, b, c, d) depend on the temperature range to which they belong;

then y along the optical path₀∈ (0, W) is expressed as:

similarly, x is taken along the optical path₀∈ (0, L) full of energy absorptionFoot:

the integrated absorption area along this path is then expressed as:

wherein, A (y)₀，v₀) And B (x)₀，v₀) The value of (b) can be obtained by experiment;

and step two, solving the formula (7):

a concentration field X (X, y) and a temperature field T (X, y) in the region D can be obtained; observing the system, one can derive:

1) although equation (7) is non-linear with respect to (X, y), T (X, y)), if T (X, y) is given, equation (7) is linear with respect to X (X, y);

2) for a given T (X, y), equation (7) is unstable with respect to X (X, y), i.e., small perturbations of (a, B) will result in large changes in X (X, y);

3) for a given X (X, y), equation (7) remains non-linear with respect to T (X, y);

according to the characteristics of the system, solving (X (X, y), T (X, y)):

1) suppose (X)^*(x，y)，T^*(X, y)) is an exact solution that satisfies the system, while giving (X)^*(x，y)，T^*(x, y)) is a priori approximatedAnd an iteration initial value (X)⁰(x，y)，T⁰(x, y)), and gives the maximum number of iterations N_maxRegularization parameters μ, β > 0, iteration termination level > 0, and an allowable set X_range×T_rangeSetting the initial value of n to be 0;

2) for known Tⁿ(X, y) X is obtained by solving the following formula through post-discretization regularizationⁿ⁺¹(x，y)：

In the formula,an operator used in the iteration is represented; if Xⁿ⁺¹(x，y)∈X_rangeTaking mu as mu₀And jumping out of this iteration; otherwise, update μ ← 2 μ, calculate X againⁿ⁺¹(x，y)；

3) For known Xⁿ⁺¹(x, y) T is obtained by solving the following formula through post-discretization regularizationⁿ⁺¹(x，y)：

In the formula,an operator used in the iteration is represented; if Tⁿ⁺¹(x，y)∈T_rangeChoose β ═ β₀And jump out of the iteration, otherwise update β ← 2 β, calculate T againⁿ⁺¹(x，y)；

4) For a sufficiently large number n, the termination criterion is satisfied:

||(Xⁿ⁺¹，Tⁿ⁺¹)-(Xⁿ，Tⁿ)||_D＜(10)；

or N ═ N_maxThe iteration terminates, (X)ⁿ⁺¹，Tⁿ⁺¹) As final solutions of concentration field and temperature field; otherwise, updating Tⁿ←T^{n +1}And n ← n +1, and repeating steps 2-4.

Step three, in order to improve the reconstruction effect, the invention provides that in each direction of the area to be measured, the information comprising a plurality of gas characteristic absorption spectral lines is fully utilized, and the center frequency corresponding to the selected r-th gas characteristic absorption spectral line is recorded as v_r. The formulae (8) and (9) and (A, B) are dependent on v_rThus, each iteration of equations (8) and (9) may be represented by:

instead of this;

and step four, carrying out grid discretization treatment on the two-dimensional area to be detected, and solving the concentration and the temperature in each grid by adopting a self-adaptive iteration method:

1) according to the shape and the size of the two-dimensional area D to be measured, the two-dimensional area to be measured is divided into M rows and N columns of grids, M is equal to N, and each grid corresponds to a value to be measured of concentration and temperature. Selecting I gas characteristic absorption spectral lines from a spectral database, wherein I is not less than 2 xMxN/(M + N), and the value of r is an integer between 1 and I;

2) equation (11.2) can be written as:

EgS(T，v_r)X＝P(v_r)(13)；

in the formula, P (v)_r) Is a spectral line v_rCorresponding measured value projection vector, E ═ E_(i，j)) Is 2N × N²0-1 matrix of dimensions, where e_(i，j)Indicating whether the laser passes through the jth grid in the ith direction, namely when the laser in the ith direction passes through the jth grid, enabling e_(i，j)1, otherwise e_(i，j)＝0；

The explicit solution of equation (13) is thus represented as:

wherein,

by the formula (14), can be represented by Tⁿ(X, y) calculating to obtain Xⁿ⁺¹(x，y)；

3) X calculated in step 2ⁿ⁺¹(x, y) as a known quantity, using the non-linear maximumT is obtained by solving equation (12) by using a quadratic optimization algorithmⁿ⁺¹(x，y)。

Wherein in order to ensure numerical convergence of the iterative solution, an allowable set X of X (X, y) and T (X, y) is given_range×T_rangeSo that it contains the exact solution X^*(x, y) and T^*(x, y) and simultaneously introducing a penalty term with the regularization parameters mu and β to overcome the ill-conditioned nature of the reconstruction process, and automatically adjusting the regularization parameters mu and β in each step of iteration so as to ensure that the iterative solution converges to an accurate solution.

Simulation embodiment

In order to test the performance of the algorithm, the invention simulates the common temperature and concentration models in practical application occasions and compares the reconstruction result of the invention with the simulated annealing algorithm result.

The temperature range of a two-dimensional rectangular area to be measured is 1000-1500K, the volume concentration range of water vapor is 0-0.2, the adopted distribution model is a double-peak curved surface, the model is constructed by overlapping a Gaussian curved surface and a parabolic curved surface, and the expression is shown as formula (16):

wherein f (x, y) is the temperature field or concentration field of the region to be measured, (x)₀，y₀，z₀) Is the peak point position, p, of the Gaussian and parabolic surfaces₁、p₂、K、b₁、b₂、c₁、c₂Are all parameters set during simulation.

As shown in fig. 2, the area to be measured is discretized into a 10 × 10 grid, in order to make the system of equations satisfy the closed solving condition, the number of the selected absorption spectral lines needs to satisfy I ≥ 10, 10 characteristic absorption spectral lines of water vapor are selected, and the specific information of each spectral line is shown in table 1; the distribution of the temperature field and the concentration field set according to the double-peak curved surface model is shown in figures 3-4, and the results of the temperature field and the concentration field reconstructed by adopting the algorithm and the simulated annealing algorithm provided by the invention are shown in figures 5-8;

table 1: 10H selected when the algorithm of the invention is used for carrying out simulation embodiment₂Absorption line information of O

As can be seen from fig. 5 to 8, in the bimodal surface model, the temperature field and the concentration field reconstructed by respectively adopting the alternating iteration algorithm and the simulated annealing algorithm are both consistent with the set values, and higher reconstruction accuracy can be realized. The calculation time of the alternating iteration algorithm provided by the invention is 6.08s, which is far shorter than the calculation time 40238.33s of the simulated annealing algorithm.

In addition, noise interference inevitably occurs during the actual measurement process. In order to verify the anti-noise capability of the alternating iteration algorithm provided by the invention, Gaussian white noise with different proportions is added to a projection absorption area obtained by a double-peak curved surface model, and the data added with the noise is utilized to reconstruct a temperature field and a concentration field. To facilitate comparison of reconstruction results, the root mean square error is defined as the evaluation criterion:

in the formula (f)_i，jIs the temperature value or concentration value at the jth cell in the ith direction, f_0(i，j)Is corresponding to f_i，jThe set value of (2). The reconstructed rms error magnitude is shown in figure 9. As can be seen from fig. 9, the alternating iteration algorithm is more stable in reconstructing the temperature field, and the noise immunity is significantly higher than that of the simulated annealing algorithm. The integral effect of the reconstruction of the temperature field and the concentration field is comprehensively considered, the alternating iteration algorithm provided by the invention has stronger anti-noise interference capability while ensuring the reconstruction quality, and is suitable for large-scale field inversion calculation。

The algorithm firstly provides a linearization scheme for the calculation of the concentration field, and semi-linearizes the original system, thereby weakening the nonlinearity of the original system; secondly, an alternative iteration scheme is provided for a temperature field and a concentration field to be measured, and the number of unknown variables is reduced by half in each step of iteration; finally, penalty terms are introduced by using an optimization technology to overcome the ill-posed characteristic of the reconstruction process, the regularization parameters can be automatically adjusted during each step of iteration, and the iterative solution is guaranteed to be converged into an accurate solution. The alternating iteration algorithm provided by the invention can obviously shorten the calculation time on the premise of maintaining the reconstruction precision, and is suitable for large-scale field inversion calculation.

Claims (4)

1. An alternating iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption is characterized by comprising the following steps:

step one, allowing the high-temperature gas to be measured to flow through a two-dimensional rectangular area, and recording the area to be measured as D { (x, y): 0 < X < L, 0 < y < W }, a temperature field T (X, y), a concentration field X (X, y), and a relationship between a laser measurement value passing through the region D and the temperature field and the concentration field in the region D is expressed by equation (1):

$\left\{\begin{array}{c}P{\&Integral;}_0^{L}X(x,y_0)S\left(T\right(x,y_0),v_0)dx=A(y,v_0),y_0\&Element;(0,W)\\ P{\&Integral;}_0^{W}X(x_0,y)S\left(T\right(x_0,y),v_0)dy=B(x,v_0),x_0\&Element;(0,L)\end{array}\right.---\left(1\right);$

in the formula, A (y)₀，v₀) Is a center frequency v₀Along a path y ═ y₀∈ (0, W) integrated absorption area measurement, B (x)₀，v₀) Is along path x ═ x₀∈ (0, L), and P is the regionGas pressure over domain D, S (T (x, y)₀)，v₀) Is a temperature T (x, y)₀) Frequency v₀The spectral line of (A) is strong;

step two, solving (X (X, y), T (X, y)) according to the formula (1):

1) suppose (X)^*(x，y)，T^*(X, y)) is an exact solution that satisfies the system, while giving (X)^*(x，y)，T^*(x, y)) is a priori approximatedAnd an iteration initial value (X)⁰(x，y)，T⁰(x, y)), and gives the maximum number of iterations N_maxRegularization parameters μ, β > 0, iteration termination level > 0, and an allowable set X_range×T_rangeSetting the initial value of n to be 0;

2) for known Tⁿ(X, y) X is obtained by solving the following formula through post-discretization regularizationⁿ⁺¹(x，y)：

$T^{n+1}(x,y)=\arg \underset{X}{\min }\left\{\right||K_L^n\&CenterDot;X-A|{|}_{(0,W)}^2+\left|\right|K_W^n\&CenterDot;X-B|{|}_{(0,L)}^2+\mathrm{\&mu;}||X-\stackrel{\&OverBar;}{X}|{|}_D^2\}---\left(2.1\right);$

$\left\{\begin{array}{c}(K_L^n\&CenterDot;X)\left(y_0\right)=P{\&Integral;}_0^{L}X(x,y_0)S\left(T^n\right(x,y_0),v_0)dx=A(y_0,v_0),y_0\&Element;(0,W)\\ (K_W^n\&CenterDot;X)\left(x_0\right)=P{\&Integral;}_0^{W}X(x_0,y)S\left(T^n\right(x_0,y),v_0)dy=B(x_0,v_0),x_0\&Element;(0,L)\end{array}\right.---\left(2.2\right);$

In the formula,an operator used in the iteration is represented; if Xⁿ⁺¹(x，y)∈X_rangeTaking mu as mu₀And jumping out of this iteration; otherwise, update μ ← 2 μ, calculate X againⁿ⁺¹(x，y)；

3) For known Xⁿ⁺¹(x, y) T is obtained by solving the following formula through post-discretization regularizationⁿ⁺¹(x，y)：

$T^{n+1}(x,y)=\arg \underset{T}{\min }\left\{\right||G_L^{n+1}\&CenterDot;T-A|{|}_{(0,W)}^2+\left|\right|G_W^{n+1}\&CenterDot;T-B|{|}_{(0,L)}^2+\mathrm{\&beta;}||T-\stackrel{\&OverBar;}{T}|{|}_D^2\}---\left(3.1\right);$

$\left\{\begin{array}{c}(G_L^{n+1}\&CenterDot;T)\left(y_0\right)=P{\&Integral;}_0^L{X}^{n+1}(x,y_0)S\left(T\right(x,y_0),v_0)dx=A(y,v_0),y_0\&Element;(0,W)\\ (G_W^{n+1}\&CenterDot;T)\left(x_0\right)=P{\&Integral;}_0^W{X}^{n+1}(x_0,y)S\left(T\right(x_0,y),v_0)dy=B(x,v_0),x_0\&Element;(0,L)\end{array}\right.---\left(3.2\right);$

In the formula，An operator used in the iteration is represented; if Tⁿ⁺¹(x，y)∈T_rangeChoose β ═ β₀And jump out of the iteration, otherwise update β ← 2 β, calculate T againⁿ⁺¹(x，y)；

4) For a sufficiently large number n, the termination criterion is satisfied:

||(Xⁿ⁺¹，Tⁿ⁺¹)-(Xⁿ，Tⁿ)||_D＜(1)；

or N ═ N_maxThe iteration terminates, (X)ⁿ⁺¹，Tⁿ⁺¹) As final solutions of concentration field and temperature field; otherwise, updating Tⁿ←Tⁿ⁺¹N ← n +1, and steps 2) to 4) are repeated.

2. The alternating iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption according to claim 1, characterized in that information including a plurality of gas characteristic absorption lines is fully utilized in each direction of the region to be measured, and the center frequency corresponding to the selected r-th gas characteristic absorption line is recorded as v_rWhereby formula (2.1), formula (2.2), formula (3.1) and formula (3.2) are replaced with formula (5.1), formula (5.2), formula (6.1) and formula (6.2), respectively:

$X^{n+1}=\arg \underset{X}{\min }\left\{\right||K_{L,r}^n\&CenterDot;X-A_r|{|}_{(0,W)}^2+\left|\right|K_{W,r}^n\&CenterDot;X-B_r|{|}_{(0,L)}^2+\mathrm{\&mu;}||X-\stackrel{\&OverBar;}{X}|{|}_D^2\}---\left(5.1\right);$

$\left\{\begin{array}{c}(K_{L,r}^n\&CenterDot;X)\left(y_0\right)=P{\&Integral;}_0^{L}X(x,y_0)S\left(T^n\right(x,y_0),v_r)dx=A_r(y_0,v_r),y_0\&Element;(0,W)\\ (K_{W,r}^n\&CenterDot;X)\left(x_0\right)=P{\&Integral;}_0^{W}X(x_0,y)S\left(T^n\right(x_0,y),v_r)dy=B_r(x_0,v_r),x_0\&Element;(0,L)\end{array}\right.---\left(5.2\right);$

$T^{n+1}=\arg \underset{T}{\min }\left\{\right||G_{L,r}^{n+1}\&CenterDot;T-A_r|{|}_{(0,W)}^2+\left|\right|G_{W,r}^{n+1}\&CenterDot;T-B_r|{|}_{(0,L)}^2+\mathrm{\&beta;}||T-\stackrel{\&OverBar;}{T}|{|}_D^2\}---\left(6.1\right);$

$\left\{\begin{array}{c}(G_{L,r}^{n+1}\&CenterDot;T)\left(y_0\right)=P{\&Integral;}_0^L{X}^{n+1}(x,y_0)S\left(T\right(x,y_0),v_r)dx=A_r(y,v_r),y_0\&Element;(0,W)\\ (G_{W,r}^{n+1}\&CenterDot;T)\left(x_0\right)=P{\&Integral;}_0^W{X}^{n+1}(x_0,y)S\left(T\right(x_0,y),v_r)dy=B_r(x,v_r),x_0\&Element;(0,L)\end{array}\right.---\left(6.2\right).$

3. the alternating iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption according to claim 2, wherein the region to be measured is subjected to grid discretization, and a self-adaptive iterative method is used to solve for the concentration and temperature in each grid, wherein the solving process is as follows:

1) dividing the two-dimensional area to be measured into M rows and N columns of grids according to the shape and the size of the two-dimensional area to be measured D, enabling M to be equal to N, enabling each grid to correspond to a value to be measured of concentration and temperature, selecting I gas characteristic absorption spectral lines from a spectral database, and enabling I to be more than or equal to [2 XMXN/(M + N) ], wherein the value of r is an integer between 1 and I;

2) equation (5.2) is written as:

EgS(T，v_r)X＝P(v_r)(7)；

in the formula, P (v)_r) Is a spectral line v_rCorresponding measured value projection vector, E ═ E_(i，j)) Is 2N × N²0-1 matrix of dimensions, where e_(i，j)Indicating whether the laser passes through the jth grid in the ith direction, and enabling e to pass through the jth grid when the laser in the ith direction passes through the jth grid_(i，j)1, otherwise e_(i，j)＝0；

The explicit solution of equation (7) is represented as:

$X^{n+1}={({A_n}^T{A}_n+\mathrm{\&alpha;}I)}^{-1}({A_n}^{T}P+\mathrm{\&alpha;}\stackrel{\&OverBar;}{X})---\left(8\right);$

wherein,

by formula (8) of Tⁿ(X, y) calculating to obtain Xⁿ⁺¹(x，y)；

3) X calculated in step 2)ⁿ⁺¹(x, y) as a known quantity, and solving equation (6.1) using a nonlinear least squares optimization algorithm to obtain Tⁿ⁺¹(x，y)。

4. The alternating iterative algorithm for temperature field and concentration field reconstruction based on spectral absorption according to claim 1, characterized in that: given an allowable set X of X (X, y) and T (X, y)_range×T_rangeSo that it contains the exact solution X^*(x, y) and T^*(x, y) and a penalty term with the regularization parameter mu, β is introduced to overcome the ill-conditioned nature of the reconstruction process, and the regularization parameter mu, β is automatically adjusted in each iteration stepThereby ensuring that the iterative solution converges to an accurate solution.